What will come in place of the question mark (?) in the following questions ?
`sqrt(11449) xx sqrt(6241) - (54)^(2) = sqrt(?) + (74)^(2)`

Options

A. 3844
B. 3721
C. 3481
D. 3638

Answer

To solve the equation \( \sqrt{11449} \times \sqrt{6241} - (54)^2 = \sqrt{?} + (74)^2 \), we will follow these steps:

### Step 1: Calculate \( \sqrt{11449} \)
To find \( \sqrt{11449} \):
- We can use prime factorization or a calculator.
- \( \sqrt{11449} = 107 \).

**Hint:** Check if the number is a perfect square by finding its prime factors.

### Step 2: Calculate \( \sqrt{6241} \)
Next, we calculate \( \sqrt{6241} \):
- Again, using a calculator or prime factorization.
- \( \sqrt{6241} = 79 \).

**Hint:** Similar to the previous step, confirm if \( 6241 \) is a perfect square.

### Step 3: Calculate \( (54)^2 \)
Now we calculate \( (54)^2 \):
- \( (54)^2 = 2916 \).

**Hint:** Remember that squaring a number means multiplying it by itself.

### Step 4: Substitute the values into the equation
Now we substitute the values we calculated into the equation:
\[ 107 \times 79 - 2916 = \sqrt{?} + (74)^2 \]

### Step 5: Calculate \( 107 \times 79 \)
Next, we calculate \( 107 \times 79 \):
- \( 107 \times 79 = 8463 \).

**Hint:** You can break it down as \( 107 \times (70 + 9) \) to simplify the multiplication.

### Step 6: Calculate \( (74)^2 \)
Now calculate \( (74)^2 \):
- \( (74)^2 = 5476 \).

**Hint:** Use the same method of squaring as in Step 3.

### Step 7: Substitute and simplify
Now we substitute back into the equation:
\[ 8463 - 2916 = \sqrt{?} + 5476 \]

### Step 8: Calculate \( 8463 - 2916 \)
Now we perform the subtraction:
\[ 8463 - 2916 = 5547 \]

**Hint:** Make sure to line up the numbers correctly for accurate subtraction.

### Step 9: Set up the equation for \( \sqrt{?} \)
Now we have:
\[ 5547 = \sqrt{?} + 5476 \]

### Step 10: Isolate \( \sqrt{?} \)
To isolate \( \sqrt{?} \):
\[ \sqrt{?} = 5547 - 5476 \]

### Step 11: Calculate \( 5547 - 5476 \)
Now calculate:
\[ 5547 - 5476 = 71 \]

### Step 12: Square both sides to find \( ? \)
Now we square both sides to find \( ? \):
\[ ? = 71^2 \]
Calculating \( 71^2 \):
\[ 71^2 = 5041 \]

### Final Answer
Thus, the value of \( ? \) is:
\[ \boxed{5041} \]